This is a preliminary version of introductory lecture notes for Differential Topology. The presentation follows the standard introductory books of Milnor and Guilleman-Pollack. The difference to Milnor's book is that we do not assume prior knowledge of point set topology. All relevant notions in this direction are introduced in Chapter 1. Also the transversality is discussed in a broader and more general framework including basic vector bundle theory. We try to give a deeper account of basic ideas of differential topology than usual in introductory texts. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail.